On the only jet engined aircraft I'm trained on, the Bell 206B (Allison 250 engine), I was taught to move the throttle slowly and smoothly, especially when opening. I've also see this done with Rolls Royce testing RB211s and early Trents.
I've realised I don't actually know why this is. Is it to prevent possible flame out with a sudden increase in fuel with no corresponding increase in air mass since the engine will spool up much more slowly?
Do modern engines need this handling? In this video at about 0:17, the pilot commences the roll by more or less slamming the throttle open. My guess is that like all other computer controlled controls, the FADEC interprets this as "as much fuel as possible without flaming out".